Finding Super-spreaders in SIS Epidemics

In network epidemic models, controlling the spread of a disease often requires targeted interventions such as vaccinating high-risk individuals based on network structure. However, typical approaches assume complete knowledge of the underlying contact network, which is often unavailable. While network structure can be learned from observed epidemic dynamics, existing methods require long observation windows that may delay critical interventions. In this work, we show that full network reconstruction may not be necessary: control-relevant features, such as high-degree vertices (super-spreaders), can be learned far more efficiently than the complete structure. Specifically, we develop an algorithm to identify such vertices from the dynamics of a Susceptible-Infected-Susceptible (SIS) process. We prove that in an $n$-vertex graph, vertices of degree at least $n^\alpha$ can be identified over an observation window of size $\Omega (1/\alpha)$, for any $\alpha \in (0,1)$. In contrast, existing methods for exact network reconstruction requires an observation window that grows linearly with $n$. Simulations demonstrate that our approach accurately identifies super-spreaders and enables effective epidemic control.